Proceedings of the Twenty-Seventh AAAI Conference on Artificial Intelligence
Teaching Classification Boundaries to Humans
Sumit Basu
Janara Christensen
Microsoft Research
Redmond, WA
sumitb@microsoft.com
University of Washington
Seattle, WA
janara@cs.washington.edu
Abstract
portant is training (calibrating) human labelers for high
inter-annotator agreement with past labelers. By teaching
new raters using labels from past raters, we can train them
to produce more consistent and thus higher quality data.
We know from both theoretical and empirical findings
that classifiers learn best from data that constitute a representative sample, i.e., a random sample that has the same
distribution as the target data. There are variations such as
active learning, in which a classifier can pick from a palette
of unlabeled points to be labeled. Humans are quite different from classifiers, though: simply seeing representative
examples does not mean they will perform optimally with
respect to them. They will be more sensitive to some features than others, they will not perfectly consider all the
information from all the samples, and they will be confused
by items that are similar. They may have “blind spots” or
inherent biases that lead them to make less than optimal
decisions. Active learning approaches where the human
could pick the next sample to be labeled may help in limited scenarios, but when there are multiple dimensions (of
features), the perplexity of possible choices could prove
overwhelming. Similarly, automatically choosing examples
that would be “best” for a classifier can be disastrous for a
human; we found this in our own pilot experiments.
Given the possible benefits and inherent questions, we
investigate in this paper what might be the best way to
teach a classification task to a human from a palette of
available methods. The obvious baseline is random presentation, i.e., picking examples from the same distribution
as the test set, but we suspected that it would be possible to
do better. We thus developed a set of mechanisms we hypothesized could be helpful to humans in the learning task,
some based on the cognitive science and machine learning
literature, others based on our models of task mastery. In
particular, these mechanisms were (1) an indicator of individual example difficulty, (2) a means of selecting examples in order of increasing difficulty (curriculum learning),
and (3) the estimation of a “coverage model” of the subject’s mastery over the data space and then sampling from
its complement. To test the effectiveness of our methods,
Given a classification task, what is the best way to teach the
resulting boundary to a human? While machine learning
techniques can provide excellent methods for finding the
boundary, including the selection of examples in an online
setting, they tell us little about how we would teach a human
the same task. We propose to investigate the problem of example selection and presentation in the context of teaching
humans, and explore a variety of mechanisms in the interests
of finding what may work best. In particular, we begin with
the baseline of random presentation and then examine combinations of several mechanisms: the indication of an example’s relative difficulty, the use of the shaping heuristic from
the cognitive science literature (moving from easier examples to harder ones), and a novel kernel-based “coverage
model” of the subject’s mastery of the task. From our experiments on 54 human subjects learning and performing a pair
of synthetic classification tasks via our teaching system, we
found that we can achieve the greatest gains with a combination of shaping and the coverage model.
Introduction
Machine learning has yielded a broad variety of impressive
results on how best to train a classifier, but what is the best
way to teach a classification task to a human? The literature
has mostly neglected this question, despite the potential for
education as well as other scenarios. This raises the question of why one might wish to teach humans this particular
type of task. Beyond the underlying questions about how
best to teach human subjects in this scenario, we believe
there are several practical applications. The first and most
direct is that of teaching a real-world discrimination task.
As humans we are often required to make such classifications: is this a safe link to click on or not, is this a safe place
to use a credit card, is this peach sufficiently ripe, is this a
morel mushroom or a poisonous false morel – if we can do
better than picking random examples for teaching such
tasks, we may be able to improve human performance in
the real world. A second scenario that is increasingly imCopyright © 2013, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
109
we developed a synthetic learning task: subjects learned to
classify parametrically drawn mushrooms based on presented examples and then took a quiz to determine how much
they learned. As a result of these experiments, we found
that indeed we can do substantially better than random
presentation with some combinations of these methods.
the correspondence to a vector space is not explicit, as with
a real-world classification task with only a similarity metric
available, and as such, we didn’t want to focus on methods
that took advantage of an explicit representation of the feature space. We also note that their methods were independent of the user’s performance during training. In their workflow, the user was shown labels for the examples they or
the algorithm picked (users were tested at intervals on the
location of the boundary); as such their performance was
not recorded or used. In our work, with every training example the subject was required to test their knowledge before the label was revealed. Our work leverages this information during training via our “coverage model.”
Another thread of related work comes from the “shaping”
work in the classic cognitive science literature via its recent
application in the machine learning community. The original work, by Skinner and others (Peterson 2004) was based
on the theory that it is possible to teach a complex
task/behavior by building up and reinforcing smaller subtasks. A generalization of this theory is that it may be more
efficient to teach a difficult concept by starting off with
easy versions of it (Kreuger and Dayan 2009). The latter
interpretation has found success in recent work on online
learning, in which easier examples are presented before
more difficult examples for online training of classifiers;
this approach is known as “curriculum learning,” as explored in (Bengio et al. 2009) and (Kumar, Packer, and
Koller 2010). Given the success of this approach in teaching classifiers (recently) and animals/humans (classically),
we added this strategy for teaching to our suite. The work
on curriculum learning led Khan, Zhu, and Mutlu (2011) to
a related investigation, though with the converse of our
goals, in which the authors studied how humans might
choose to teach a classifier (robot).
In summary, other than (Castro et al. 1980), ours is the
only work we are aware of to teach classification boundaries, and the first to teach higher dimensional boundaries.
Related Work
There is a wealth of literature on the general area of teaching with the help of computers, an area known as Interactive Tutoring Systems, but most of this work is focused on
aiding with traditional classroom curricula; the recent compilation of Woolf (2008) provides an excellent overview.
The closest to our topic is the work on teaching categories,
specifically in the context of teaching vocabulary. The emphasis in that research has been on spacing effects, i.e., selecting the interval of study to maximize retention; see for
instance the recent work of Mozer et al. (2009). If we reach
further afield into the cognitive science literature, there is
much work examining how humans form and learn categories, like the classic work of Markman (1989).
The closest research to our own appears in the machine
learning literature, in an investigation by Castro et al.
(2008) which sought to examine how active learning heuristics would fare in the context of teaching humans. As active
learning is focused on finding the best order of examples to
present to an online learning algorithm (see (Settles 2010)
for a current review of active learning), it was a natural
choice to apply these algorithms to humans. The authors
presented subjects with a 1-D (single parameter) classification problem, where their goal was to identify the location
of the boundary. Subjects were shown examples with the
parameter illustrated with synthetic “eggs” of varying
shapes. They found the best results came via an approach
they termed “yoked learning,” in which they bisected the
posterior for the location of the boundary at each step given
the presented examples, getting ever closer to the solution.
We note that in 1-D, the boundary is just a point, whereas in
higher dimensions (such as in our experiments), the boundary is an N-1 dimensional hyperplane, and there is no corresponding bisection approach. While such a method could be
used to find a single point on the boundary, our goal is to
teach the human the difference between the classes, and for
that they need to know the entire classification boundary.
Another approach Castro et al. found helpful was letting
humans choose the next location to view. Again, that makes
sense in a 1-D space – subjects can quickly converge on the
boundary. In the 4-D space of our experiments there are far
too many possibilities, and no simple way for subjects to
visualize the space. In our study, we had 10,000 points
sampled uniformly from the space, and showing all of these
or even a representative sample in a random ordering would
be quite overwhelming. Furthermore, we were also interested in the case where the feature space could be latent, i.e.,
Learning Task
For this study, we wanted to choose a classification task of
sufficient complexity that users would not master it with a
few examples, but not so difficult that it would take egregiously long to learn. We also wanted to be able to generate
a large number of unique learning problems of equivalent
difficulty; as such we focused on using synthetic data with
randomly selected boundaries. Through extensive piloting,
we found 4-dimensional data to be a good compromise:
subjects could quickly get a good understanding of the
problem without saturating their performance too early.
As we wished to make the task as natural as possible, we
chose to represent the data as parametrically drawn mushrooms instead of directly showing the numerical values of
the four-dimensional instances (see Figure 1). The four di-
110
mensions, all between 0 and 1, were mapped to ranges of
the stem width, stem height, cap width, and the cap height.
small colored square in the upper right corner of the view
(see Figure 2). The color varied from bright green (easy) to
bright red (hard). The difficulty value was computed as the
negative of the projected absolute distance to the boundary,
normalized to be between 0 (easiest) and 1 (hardest):
| |
In this formulation, z is a normalizing constant equal to the
maximum possible value for given the choice of w.
Curriculum Learning
Our next proposal originated from the cognitive science
work in shaping as well as the machine learning work in
curriculum learning, i.e., the idea that one could train a
learner more efficiently by presenting easier examples first
and then showing progressively harder examples. For our
study, we used the same measure shown above for the difficulty indicator. For any given training example number, we
chose a linearly related to the example number, such
that the maximum hardness was achievable by the 20th example (out of 30). Examples were still drawn randomly, but
if the drawn instance had difficulty greater than , it
was returned to the set and a new example was chosen. This
process continued until an example was found with difficulty less than . We also added a balance constraint that
prevented the difference between the number of seen positive and negative examples to be no more than one.
Figure 1: Examples of parametrically drawn mushrooms.
The classification boundary was an N-1 dimensional hyperplane; we did not add any label noise, and as such the problems were linearly separable. In order to ensure that the
tasks would be of equal difficulty and that random guessing
would result in a base rate of 50% on average, we required
the boundary to pass through the origin. Formally, we randomly chose a 4-dimensional w, normalized it to unit
length, and computed the label for each exemplar as 1 if
0 and 0 otherwise. As such, we were able to construct a new problem for every task and every subject: for
each trial we would begin by sampling 10,000 points from a
uniform distribution and then generating a boundary.
Teaching Methods
Coverage Model
As our goal was to investigate what methods might work
best for teaching, we developed several mechanisms to
compete with our baseline of random presentation.
Difficulty Indicator
Our final scheme for improving learning involved what we
term a “coverage model:” we model the areas of the example space in which the subject had gained expertise, and
then sample from the complement of that distribution. This
method has analogies to the boosting approach of classifier
combination, in which examples where the classifier performs poorly are reweighted to focus the efforts of successive learners (Freund and Schapire 1999). As we are not
doing batch learning, we cannot explicitly apply the reweighting used in boosting, but instead use a kernel-based
approach to represent the expertise distribution and use it to
guide example selection.
Since points near each other would be similar in mushroom appearance and typically in label, we modeled the
user’s knowledge as a mixture of Gaussian kernels of fixed
variance. The kernel centers were at every point the subject
had been given a training example, as well as 100 random
samples chosen from the unlabeled points to prevent overfitting. The form of the function was as follows:
1
; , 0
The first mechanism we considered was an indicator for the
difficulty of a given training example. This was shown as a
The set represents the indices of the examples that have
been labeled by the subject during training, the set ! is the
Baseline
We initially considered two baseline methods, random
presentation and the active learning heuristic of the points
closest to the boundary. We initially included the boundary
method as well because it seemed like a good instance of a
scheme that was ideal for a learning algorithm but terrible
for human learners attempting to perform a classification
task. Our intuition was correct: in an experiment with a
three-dimensional feature space (also represented as a
mushroom), a set of 13 users achieved 53.6% performance,
far worse than random presentation (on which they
achieved 71.7%), a difference that was significant (twotailed t-test, unequal variances: p=0.001, df=22.7, t=3.76).
Furthermore, subjects complained bitterly about how frustrating and confusing this condition was. As its inferiority
was clear, we left out this method for the final experiment.
∈,
111
randomly selected set of 100 unseen examples, is a normalizing constant such that the distribution sums to one
over all possible examples, and is a fixed kernel width
that we determined via pilot experiments. We require the
to be positive to ensure that is positive everywhere.
We define the probability of coverage (user knowledge)
to be 1 on those indices in that the user labeled correctly, 0
on those that she labeled incorrectly, and 0.5 on those in !
(which have not been seen yet). Since we only have target
values at these points, we can solve this as an + ! dimensional discrete minimization problem:
# ‖% &‖ &'(, )* ; + , ther training during the testing period. Finally, the hardness
indicator is never shown on new examples during testing.
Experiments
We recruited a total of 90 subjects at our institution; 54
completed the entire study. As we found individuals’ capabilities varied widely in our pilot studies, we used a withinsubjects design in which each subject went through two
train/test conditions, the baseline and one other condition.
Each condition had a different class boundary for each user.
In this way, we were able to measure the relative performance of a given individual between the baseline and one
of our methods. To protect against ordering effects, we presented the two conditions in random order.
There were a total of five teaching methods; each subject
experienced the baseline as well as one other method.
• Base: training examples were chosen randomly.
• Ind: the difficulty indicator was shown; examples were
chosen randomly.
• Covg: the coverage model was used to select examples.
• IndCurr: the difficulty indicator was shown, and examples were filtered by difficulty using the curriculum
learning approach as described above.
• IndCurrCovg: the difficulty indicator was shown; examples were chosen via the coverage model and also filtered
by difficulty via curriculum learning.
Subjects were divided into the four possible condition pairs
based on the order they started the task; as not all completed the task, there is some variance in the number of subjects
(see Table 1). Each subject completed two learning tasks,
each with 30 training examples followed by 20 test; the test
examples were always drawn from a uniform distribution.
They then filled out a short survey about the tasks.
In this expression, # is the loss function, and % is the
vector of target probabilities. To constrain the to be positive, we parametrize them as , . We can then take partial
derivatives of the loss with respect to , via the chain rule:
#
2& & %
2,
,
Given these partials, we use L-BFGS Quasi-Newton optimization (Nocedal 1980) to minimize the loss.
Results and Analysis
Given the data from the subjects, we sought to understand
the differences in performance as well as what may have
led to those differences. Below, we consider subjects’ performance and perceptions under the various conditions.
Figure 2: The teaching interface.
Teaching Interface
Relative Performance by Condition
We designed a teaching interface to test the different methods with our human subjects (Figure 2), consisting of three
vertical panes. During training, the leftmost pane shows the
current training example, along with buttons with which the
subject can indicate whether it is “safe” or “poisonous.”
The interface then reveals the answer, and places the example into the appropriate (safe/poisonous) history pane. The
subject can thus review past training examples when making future judgments during both training and testing.
There are some important differences to the workflow
during testing. First, the subject is not told whether her individual answers are correct, nor are examples added to the
history panes; this is to prevent the subject from doing fur-
The core results of our study are in terms of relative performance on the test set between each of the teaching conditions and the baseline. We used the dependent t-test for
paired samples (two-sided) to compare the subjects’ performance in the two conditions they saw (Table 1). The first
two (Ind and Covg) did not show significant differences
from the baseline, though Ind had a nearly-significant negative effect. While not conclusive, it seems possible that the
difficulty indicator on its own may have hurt subjects’ performance. We hypothesize this might have been due to subjects ignoring more difficult training examples as being too
hard, or being frustrated by wildly fluctuating difficulty.
112
p
d.f.
(N-1)
t
Improve
ment
Base vs. Ind
0.12
12
-1.71
-0.09
Base vs. Covg
0.43
13
-.81
-0.05
Base vs. IndCurr
0.08
15
1.88
0.08
Base v. IndCurrCovg
0.007
10
3.36
0.12
Method
While both the IndCurr and IndCurrCovg conditions
have the benefit of curriculum learning, we believe the
greater gain in the latter is coming from the coverage model’s ability to model and highlight areas the subject performed poorly in or had not covered. This may be allowing
the subject to continue learning longer, whereas the other
models may start presenting examples that are redundant.
Table 1: Test performance improvements (mean differences in
per-condition accuracy scores across subjects) with respect to
baseline. Statistically significant results (p<0.1) are in bold.
The last two conditions, IndCurr and IndCurrCovg, did
produce significant improvements; the strongest effect was
for IndCurrCovg, both in magnitude (12 points absolute
improvement, from 61% to 73%) and in significance
(p=0.007). This implies that the coverage model in conjunction with curriculum learning has a stronger effect on performance than either on their own. In the remainder of our
analysis, we will examine the fine-grained differences in
behavior and performance to better understand these results.
Figure 4: Mean cumulative subject performance during training for the Base vs. IndCurrCovg condition (N=11).
Distribution of Training Example Difficulty
Given the difference in effect of the coverage model in the
IndCurrCovg condition vs. the Covg condition, we suspected that without restriction, the model might quickly converge onto the most difficult examples and confuse the user.
In Figure 5, we examine the distribution of examples for
Base, Covg, and IndCurrCovg over quartiles of difficulty.
For IndCurrCovg, it is biased towards easier examples. For
Covg, though, it is indeed biased in the other direction.
0.6
Base
Covg
IndCurrCovg
0.55
0.5
Figure 3: Mean cumulative subject performance during training for the Base vs. IndCurr condition (N=16).
0.45
0.4
0.35
Performance During Learning
0.3
0.25
Our first area of investigation involves seeing how subjects
performed during training by looking at their cumulative
training performance (over all examples presented so far).
In Figures 3 and 4, we look at the mean performance across
subjects for the IndCurrCovg and IndCurr conditions.
In both sets of conditions, we see that when subjects are
in the baseline condition, their performance improves for
the first few examples, but then saturates by example 15 or
so. For IndCurr, they do better earlier on and improve in
the same way but also saturate in performance at a similar
point, albeit at a higher level. For IndCurrCovg, on the other hand, we see what appears to be a faster and longer rise
in performance before learning saturates.
0.2
0.15
0.1
0.05
0
0.0 - 0.25
0.25 - 0.5
0.5 - 0.75
0.75 - 1.0
Difficulty of Training Example
Figure 5: Distributions of training example difficulties.
Performance vs. Example Difficulty
We next wished to investigate how the different strategies
affected performance at different levels of example difficulty during testing. We plotted the relative performance for
113
Survey Results
condition pairs over quartiles of difficulty in Figures 6-8.
Both IndCurrCovg and IndCurr show improvements over
Base across all levels. We also show the relative performance for the Base vs. Covg condition in Figure 8 to investigate why the coverage model was not helpful on its own.
Note that while performance for medium hardness increased slightly, performance on the easiest examples
dropped substantially. This is potentially a consequence of
the more difficult training examples shown in this case (see
Figure 5); the fact that the users did worse on the easiest
examples implies they did not learn the concept well at all.
Test Accuracy
Finally, we examine the qualitative feedback from users. In
Table 2 we look at the answers to “which condition was
more enjoyable?” and in Table 3 “which condition was easier?” Subjects overwhelmingly felt the IndCurrCovg condition was better in both respects: the mechanism that most
improved performance, then, also improved most user experience, perhaps because of the greater feeling of mastery.
We see this to a lesser extent for IndCurr as well.
The results for the other two methods were also interesting: subjects were split on both questions for Base vs. Covg,
consistent with their performance. In Base vs. Ind, on the
other hand, subjects overwhelmingly preferred the baseline.
This adds to our earlier suspicions that the difficulty indicator may have led to confusion and/or frustration.
Base
Other
Same
Base vs. Ind
9
3
0
Base vs. Covg
5
7
2
Base vs. IndCurr
2
12
3
Base vs. IndCurrCovg
3
8
0
Table 2: Survey results for the question “Which condition was
more enjoyable?
Figure 6: Test perf. vs. difficulty: Base vs. IndCurrCovg.
Base
Other
Same
Base vs. Ind
9
3
0
Base vs. Covg
5
6
3
Base vs. IndCurr
4
11
2
Base vs. IndCurrCovg
1
9
1
Table 3: Survey results for the question “Which condition was
easier?”
Discussion and Future Work
While teaching classification tasks to humans is different
from teaching algorithms, it is encouraging to see that some
ideas from machine learning are indeed helpful. Given the
strong, highly significant (p=0.007) effect on performance,
we can say with some confidence that the combination of
the difficulty indicator, curriculum learning, and the coverage model (IndCurrCovg strategy) does improve subjects’
performance at learning classification boundaries. With less
confidence, we can say that the IndCurr strategy (difficulty
indicator and curriculum learning) improves performance as
well. As such, it seems the combination of curriculum
learning and the coverage model are more powerful than
either on its own, as the Covg condition did not produce a
significant change in performance. As we had suspected
upon seeing the results, the coverage model on its own
seemed to emphasize examples that were too hard, whereas
when coupled with curriculum learning it helped subjects
Test Accuracy
Figure 7: Test performance vs. difficulty: Base vs. IndCurr.
Figure 8: Test performance vs. difficulty: Base vs. Covg.
114
Bengio, Y., Louradour, J., Collobert, R., and Weston, J. Curriculum Learning. In Proceedings of ICML 2009 (2009).
Castro, R., Kalish, C., Nowak, R., Qian, R., Rogers, T., and Zhu,
X. Human Active Learning. In Proceedings of NIPS 2008 (2008).
Freund, Y. and Schapire, R. E. A Short Introduction to Boosting.
Journal of the Japanese Society for Artificial Intelligence 14, 5
(1999), 771-780.
Khan, F., Zhu, X., and Mutlu, B. How Do Humans Teach: On
Curriculum Learning and Teaching Dimension. In Proceedings of
NIPS 2011 (2011).
Kreuger, K.A., and Dayan, P. Flexible Shaping: How Learning in
Small Steps Helps. Cognition 110, 3 (2009), 380-94.
Kumar, M.P., Packer, B., and Koller, D. Self-Paced Learning for
Latent Variable Models. In Proceedings of NIPS 2010 (2010).
Markman, E. M. Categorization and Naming in Children: Problems of Induction. MIT Press, (1989).
Mozer, M.C., Pashler, H., Cepeda, N., Lindsey, R., and Vul, E..
Predicting the optimal spacing of study: A multiscale context
model of memory. In Proceedings of NIPS 2009 (2009).
Nocedal, J. Updating Quasi-Newton Matrices with Limited Storage. Mathematics of Comp. 35 (1980), 773-782.
Peterson, G.B. A Day of Great Illumination: B.F. Skinner’s Discovery of Shaping. Journal of Experimental Analysis of Behavior
82 (2004), 317-28.
Settles, B. Active Learning Literature Survey. University of Wisconsin-Madison Computer Science Technical Report 1648,
(2010).
Woolf, B.P. Building Intelligent Interactive Tutors. Morgan
Kaufmann. (2008).
address their areas of difficulty while not overwhelming
them with hard examples early on.
The difficulty indicator, while intuitively a helpful additional source of information about each training example,
seemed to both reduce subject’s performance (though not
quite statistically significant in effect) and their enjoyment,
as well as increasing their perception of task difficulty. We
hypothesize that subjects became frustrated with and/or
ignored examples marked as difficult, and suspect this condition was particularly vexing in the absence of curriculum
learning, since hard and easy examples would be appearing
in random sequence. Perhaps seeing the hardness increase
in a controlled way (in the IndCurrCovg condition) reduced
or removed the negative effects of the indicator. However,
it’s also possible that removing the indicator and running a
CurrCovg condition would show even greater gains; we
hope to investigate this in future work. It may be that subjects are happier and learn better when they simply don’t
know the relative difficulty of the training example; this
could have interesting ramifications for other educational
domains as well.
As we outlined earlier, we believe there are a variety of
applications for which teaching classification boundaries to
humans can be important: we hope these methods and results can be helpful in such contexts, but also that they may
extend to a broader set of teaching problems.
References
Andrews, R., Diederich, J., and Tickle, A.B. Survey and Critique
of Techniques for Extracting Rules from Trained Artificial Neural
Networks. Knowledge Based Systems. 8(6) 373-389. (1995).
115